Can veet cause vaginal dryness

Yes, it can and not only dryness, it can also cause lots of irritation and vaginal infections. Veet and similar hair removal products have a lot of chemicals, it's okay to use on your legs and under your arms. But the vulva (labia and clitoris) and the vagina are very sensitive, if you use these hair removal products on your vulva it will mess with the chemical balance of your vulva and vagina which can cause the dryness you are talking about, as well as lots of itching, burning and infections.

I recommend you to shave, wax or trim instead of using Veet.